This was the "mundane" match Sir Alex Ferguson wanted put away professionally before Tuesday evening's encounter with Real Madrid in the Champions League here. Shinji Kagawa, who performed poorly in the opening leg of the last-16 tie, did the trick for Ferguson and his case for another tilt at José Mourinho's side no harm with an impressively taken hat-trick, before Wayne Rooney's late goal.

It was a win that exerts more pressure on Manchester City as the champions travel to Aston Villa on Monday evening 15 points behind and knowing that anything but victory and United can start preparing the celebratory bunting for title No20. Ferguson said: "It's a lead and we're better off than we were yesterday because we are one game less and we've won our game. That's important. We've got a cushion, I expect City to win on Monday against Villa."

With Real defeating Barcelona for the second in time in under a week, at the Bernabéu, both sides are flying, and enter Tuesday's game poised at 1-1, meaning United have what could prove a vital away goal.

This was their fourth consecutive clean sheet in the league, and Ferguson said: "It's vital, vital. If I thought we could get a blank against Real on Tuesday, we'd go through. But I think both teams will score and I hope we score more than them. It's going to be fantastic, two of the greatest teams in the world, the atmosphere will be electric, it'll be a great game. It can't be anything else but a good game."

Of Kagawa, the Scot said: "He is a good finisher. His [knee] injury in October set him back a bit, but he's getting his form back slowly and gradually. His second and third, in particular, were terrific."

The Japanese stroked home his opener in added time at the end of the first half to give United a lead that their dominance, if not end product thus far, deserved. Antonio Valencia cut back on to his left foot and swung in a cross from the right that Robin van Persie took a stab at with a boot. The ball popped up to Kagawa who was near Mark Bunn's goal and he scored the third of his debut season.

The absence of Ryan Giggs from the matchday 18 may have disappointed aficionados who hoped he would make a 1,000th appearance, though Ferguson confirmed the Welshman will have a role against Real. "He'll be involved on Tuesday, we couldn't miss that moment for the lad, he deserves it," the manager said.

The great game of guessing who Ferguson fields on Tuesday began in earnest here. Clues could be found in the blend of frontline operators chosen, including Rooney, Van Persie and Michael Carrick, alongside the second-tier players – Anderson, Valencia, Chris Smalling and Kagawa.

For the first time this season Ferguson plumped for a 4-3-3 shape, in which Carrick in midfield split Anderson (on the right) and Kagawa, and up front Van Persie was flanked by Rooney (to the left) and Valencia.

Carrick ran the game for United, particularly during the first half. This was done via an exhibition of vision and passing that continually opened up the opposition and the contest for his team. One ball to Kagawa that slid him in through traffic to Norwich's area drew applause from the home congregation. Another from near his own goal had United springing forward as Valencia raced down the right.

Giggs, who sat through the first half alongside Paul Scholes, did not return after the break. What he missed was Chris Hughton's team finally offering a threat before Kagawa confirmed the result.

Russell Martin, the visiting right-back, aimed a menacing cross at Robert Snodgrass that Nemanja Vidic scrambled away. Snodgrass then fired in a ball that worried the home rearguard.

After Rooney shot when he might have played in Van Persie, the Dutchman was taken off with Real in mind – "We agreed he would get an hour," Ferguson said.

Kagawa benefited from the class of Rooney for his second. Carrick launched a Hail Mary of a ball that bounced expertly into the Liverpudlian's path. Shaping to shoot, he swept Sébastien Bassong aside with what was revealed as a dummy. Rooney looked up, saw Kagawa's precisely judged run into the area, and squared the ball to him: the wrongfooting finish with the side of his boot gave Bunn no chance.

Kagawa's third came as Norwich wilted. He began the move, passing to Danny Welbeck, who moved the ball to Rooney and when the Japanese collected, he finished coolly.

As thoughts turned to Tuesday, Rooney was given possession by Welbeck 30 yards out. He skipped to the right, then fired a bullet past Bunn and that was 4-0 and job sweetly completed for Ferguson and his men.